richardson_extrap
Estimate order of convergence of a response as model fidelity increases
Specification
Alias: None
Arguments: None
Child Keywords:
Required/Optional 
Description of Group 
Dakota Keyword 
Dakota Keyword Description 

Required (Choose One) 
Verification Mode 
Compute the best estimate of the convergence order from three points 

Refine until the estimated covergence order converges 

Refine until the response converges 

Optional 
Rate at which the state variables are refined 

Optional 
Stopping criterion based on objective function or statistics convergence 

Optional 
Number of iterations allowed for optimizers and adaptive UQ methods 

Optional 
Identifier for model block to be used by a method 
Description
Solution verification procedures estimate the order of convergence of the simulation response data during the course of a refinement study. This branch of methods is new and currently only contains one algorithm: Richardson extrapolation.
Refinement of the model
The model fidelity must be parameterized by one or more continuous state variable(s).
The refinement path is
determined from the initial_state
of the continuous_state
variables specification in combination with the
refinement_rate
, where each of the state variables is treated as an
independent refinement factor and each of the initial state values is
repeatedly divided by the refinement rate value to define new
discretization states.
Results
Three algorithm options are currently provided:
estimate_order
converge_order
converge_qoi
Stopping Criteria
The method employs the
max_iterations
and convergence_tolerance
method independent
controls as stopping criteria.
Theory
In each of these cases, convergence order for a response quantity of interest (QoI) is estimated from
where \(r\) is the uniform refinement rate specified by
refinement_rate
.